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Bi-objective Bayesian optimization of engineering problems with cheap and expensive cost functions

(2023) ENGINEERING WITH COMPUTERS. 39(3). p.1923-1933
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Abstract
Multi-objective optimization of complex engineering systems is a challenging problem. The design goals can exhibit dynamic and nonlinear behaviour with respect to the system's parameters. Additionally, modern engineering is driven by simulation-based design which can be computationally expensive due to the complexity of the system under study. Bayesian optimization (BO) is a popular technique to tackle this kind of problem. In multi-objective BO, a data-driven surrogate model is created for each design objective. However, not all of the objectives may be expensive to compute. We develop an approach that can deal with a mix of expensive and cheap-to-evaluate objective functions. As a result, the proposed technique offers lower complexity than standard multi-objective BO methods and performs significantly better when the cheap objective function is difficult to approximate. In particular, we extend the popular hypervolume-based Expected Improvement (EI) and Probability of Improvement (POI) in bi-objective settings. The proposed methods are validated on multiple benchmark functions and two real-world engineering design optimization problems, showing that it performs better than its non-cheap counterparts. Furthermore, it performs competitively or better compared to other optimization methods.
Keywords
MULTIOBJECTIVE OPTIMIZATION, EXPECTED IMPROVEMENT, ALGORITHM, DESIGN, PAREGO, MODEL, Multi-objective optimization, Bayesian optimization, Hypervolume, Gaussian process

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Citation

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MLA
Satrio, Nasrulloh Ratu Bagus, et al. “Bi-Objective Bayesian Optimization of Engineering Problems with Cheap and Expensive Cost Functions.” ENGINEERING WITH COMPUTERS, vol. 39, no. 3, 2023, pp. 1923–33, doi:10.1007/s00366-021-01573-7.
APA
Satrio, N. R. B., Couckuyt, I., Garbuglia, F., Spina, D., Van Nieuwenhuyse, I., & Dhaene, T. (2023). Bi-objective Bayesian optimization of engineering problems with cheap and expensive cost functions. ENGINEERING WITH COMPUTERS, 39(3), 1923–1933. https://doi.org/10.1007/s00366-021-01573-7
Chicago author-date
Satrio, Nasrulloh Ratu Bagus, Ivo Couckuyt, Federico Garbuglia, Domenico Spina, Inneke Van Nieuwenhuyse, and Tom Dhaene. 2023. “Bi-Objective Bayesian Optimization of Engineering Problems with Cheap and Expensive Cost Functions.” ENGINEERING WITH COMPUTERS 39 (3): 1923–33. https://doi.org/10.1007/s00366-021-01573-7.
Chicago author-date (all authors)
Satrio, Nasrulloh Ratu Bagus, Ivo Couckuyt, Federico Garbuglia, Domenico Spina, Inneke Van Nieuwenhuyse, and Tom Dhaene. 2023. “Bi-Objective Bayesian Optimization of Engineering Problems with Cheap and Expensive Cost Functions.” ENGINEERING WITH COMPUTERS 39 (3): 1923–1933. doi:10.1007/s00366-021-01573-7.
Vancouver
1.
Satrio NRB, Couckuyt I, Garbuglia F, Spina D, Van Nieuwenhuyse I, Dhaene T. Bi-objective Bayesian optimization of engineering problems with cheap and expensive cost functions. ENGINEERING WITH COMPUTERS. 2023;39(3):1923–33.
IEEE
[1]
N. R. B. Satrio, I. Couckuyt, F. Garbuglia, D. Spina, I. Van Nieuwenhuyse, and T. Dhaene, “Bi-objective Bayesian optimization of engineering problems with cheap and expensive cost functions,” ENGINEERING WITH COMPUTERS, vol. 39, no. 3, pp. 1923–1933, 2023.
@article{8738882,
  abstract     = {{Multi-objective optimization of complex engineering systems is a challenging problem. The design goals can exhibit dynamic and nonlinear behaviour with respect to the system's parameters. Additionally, modern engineering is driven by simulation-based design which can be computationally expensive due to the complexity of the system under study. Bayesian optimization (BO) is a popular technique to tackle this kind of problem. In multi-objective BO, a data-driven surrogate model is created for each design objective. However, not all of the objectives may be expensive to compute. We develop an approach that can deal with a mix of expensive and cheap-to-evaluate objective functions. As a result, the proposed technique offers lower complexity than standard multi-objective BO methods and performs significantly better when the cheap objective function is difficult to approximate. In particular, we extend the popular hypervolume-based Expected Improvement (EI) and Probability of Improvement (POI) in bi-objective settings. The proposed methods are validated on multiple benchmark functions and two real-world engineering design optimization problems, showing that it performs better than its non-cheap counterparts. Furthermore, it performs competitively or better compared to other optimization methods.}},
  author       = {{Satrio, Nasrulloh Ratu Bagus and Couckuyt, Ivo and Garbuglia, Federico and Spina, Domenico and Van Nieuwenhuyse, Inneke and Dhaene, Tom}},
  issn         = {{0177-0667}},
  journal      = {{ENGINEERING WITH COMPUTERS}},
  keywords     = {{MULTIOBJECTIVE OPTIMIZATION,EXPECTED IMPROVEMENT,ALGORITHM,DESIGN,PAREGO,MODEL,Multi-objective optimization,Bayesian optimization,Hypervolume,Gaussian process}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{1923--1933}},
  title        = {{Bi-objective Bayesian optimization of engineering problems with cheap and expensive cost functions}},
  url          = {{http://doi.org/10.1007/s00366-021-01573-7}},
  volume       = {{39}},
  year         = {{2023}},
}

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